my first thought was that give should be actually given (I will have Peter given me a hand) as part of the future perfect, but apparently is not that type of future, and I was not able to do this exercise - I left it blank.

What is the grammar behind this ?

edit: I just have discovered there's this other Stack exchange site https://ell.stackexchange.com/ - if you consider this questions belongs there, please feel free to flag it

'I will have Sally [do X]' takes a bare infinitive and possibly object (do the dishes / make dinner / phone you / sing / come over ...). 'I will have Sally give John a hand' uses a more complicated verbo-nominal structure (give a hand) and a transitive one at that, but the causative structure (have someone [do / sing / phone ...]) still requires a bare infinitive.
– Edwin AshworthNov 26 '17 at 16:07

1 Answer
1

to have somebody do something is a very common grammar pattern in English. And that's exactly what you've got there. It simply means to get somebody to do something for you. There is nothing in your sentence that has anything to do with the future perfect tense. Just learn this piece of grammar and you're good to go.